Hysteresis modeling for smart materials and observer design for 2DOF robots

The thesis deals with the development of a new hysteresis model and the design of observers for systems with non-monotonic nonlinearities and for a clas of two-degre-of-fredom Euler- Lagrange systems (2-DOF robot). Hysteresis modeling is useful to design new smart-materials based devices, as Nitinol stent of comon use nowadays in many surgical aplications, and to improve the control of hysteretic actuators. The new model, named generalized constructive model, is able reproduce a wider clas of hysteresis nonlinearities than some of the most known models as the Clasical Preisach, the Nonlinear Preisach and the Prandtl-Ishlinski (PI) models, describing a larger number of materials. The new model is developed by an algorithm that makes use of hysteresis minor lop chords, minor lops arisen from reversal branches up to n-order. This aproach that does not make use of analytic functions, adjusting their parameters fit experimental measurements, alows to relax the hysteresis properties of equal minor lops and equal vertical chords, required by the Clasical and the Nonlinear Preisach models, buthat do not hold for a number of smart materials. Four version of the model have ben described analyzed and new les constraining properties have ben introduced to state the representation theorems of the model. The price to be paid for such wider aplicability and precision are the greater experimental measurements that ned to be colected. By mean of numerical simulations acuracy new model is compared with respecto the Clasical, Nonlinear and PI models, showing higher precision, even in the case of the experimental hysteresis temperature versus electrical resistivity of the Nitinol wire shape memory aloy. Numerical solutions for the model implementation and a rate-dependent version, for hystereses that depend also by the input rate, are proposed. To complete first part of the thesis, an academic example of a two link planarobot, which motors have ben idealy substituted by shape memory aloy actuators, show the importance of the hysteresis modeling to control such actuators. The second part of the thesis deals with reduced order observer design for nonlinear systems. observer design is derived aplying the Imersion and Invariance (I&I) technique, recently introduced in literature. This technique alows to estimate a subset of the system variables overcoming isues arisen by high gain aproaches. The design requires solution of partial diferential equations (PDEs) joined to the estimation eror definition and dynamics. This technique, asumed that solutions PDEs are obtained, is more general and alow to cope with systems for which other clasic aproaches, as the ones based on the pasivity of the estimation eror system and circle criteria based, fail for conservativenes. Then, it has ben defined a global observer for a clas of systems with non-monotonic nonlinearities, and in particular for clas of Euler-Lagrange systems with tre like mechanical configurations (robots), achieving global convergence of thestimation eror. A separation principle for the later systems is proposed with computed torque and nonlinear PD-like terms controlaw by mean of Lyapunov-based tols. Numerical simulationshown the performances of the proposed observer and the output fedback design.